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Cubes and Dice Questions

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Four usual dice are thrown on the ground. The total of numbers on the top faces of these four dice is 13 as the top faces showed 4, 3, 1 and 5 respectively. What is the total of the faces touching the ground?.PNG" alt="cube-dice-4443" style="width:288px;height:235px;">


A12

B13

C15

DCan not be determined

ENone of these

Answer: Option C

Explanation:

In a usual dice, the sum of the numbers on any two opposite faces is always 7. Thus, 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.

Consequently, when 4, 3, 1 and 5 are the numbers on the top faces, then 3, 4, 6 and 2 respectively are the numbers on the face touching the ground. The total of these numbers = 3 + 4 + 6 + 2 = 15.

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Two positions of a dice are shown below. If the face with 1 dot is at the bottom, then the number of dots on the top is
cube-dice-3534


A2

B3

C4

D5

ENone of these

Answer: Option B

Explanation:

From figures (i) and (ii), we conclude that 5, 4, 6 and 2 dots appear adjacent to 3 dots. Therefore, 1 dot must appear opposite 3 dots. Thus, if the face with 1 dot is at the bottom, then the face with 3 dots will appear on the top.

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What number is opposite 3 in the figure shown below? The given two positions are of the same dice whose each surface bears a number among 1, 2, 3, 4, 5 and 6.
cube-dice-1514


A2

B4

C5

D6

ENone of these

Answer: Option C

Explanation:

From figures (i) and (ii), we conclude that 2, 6, 1 and 4 appear adjacent to 5. Therefore, 3 must appear opposite 5, Conversely, the number opposite 3 is 5.

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A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.
cube-dice-65


A3

B4

C5

D6

ENone of these

Answer: Option C

Explanation:

From figures (i), (ii) and (iv) We conclude that 6, 4, 3 and 1 lie adjacent to 2. Hence, 5 must lie opposite 2.

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A dice is numbered from 1 to 6 in different ways.
If 2 is opposite to 3 and adjacent to 4 and 6, then which of the following statements is necessarily true?.PNG" alt="cube-dice-1817" style="width:288px;height:235px;">


A1 is opposite to 5

B4 is opposite to 6

C4 is adjacent to 2 and 6

D1 is adjacent to 2 and 3

ENone of these

Answer: Option D

Explanation:

If 2 is opposite to 3, then 1 cannot lie opposite to either of the two numbers - 2 or 3. Hence, 1 is necessarily adjacent to both 2 and 3.

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Three positions of a dice are given. Based on them find out which number is found opposite the number 2 in the given cube.
cube-dice-54


A6

B5

C3

D1

ENone of these

Answer: Option A

Explanation:

From figures (i) and (ii), we conclude that the numbers 1, 4, 3 and 5 lie adjacent to the number 6. Clearly, the number 2 lies opposite 6 and conversely 6 lies opposite 2.

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Two positions of a cube are shown below. When the number 4 will be at the bottom, then which number will be at the top?
cube-dice-2019


A3

B5

C6

DCan not be determined

ENone of these

Answer: Option A

Explanation:

Number 1 is common to both the positions of the dice. We assume the dice in fig. (ii) to be rotated so that 1 remains on the RHS face (i.e. face II as per activity 1) and the numbers 5 and 3 move to the faces hidden behind 2 and 4 respectively (in fig. (i). Then, clearly 3 lies opposite 4. Hence, when 4 is at the bottom then 3 mist lie on the top.

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The six faces of a dice have been marked with alphabets A, B, C, D, E and F respectively. This dice is rolled down three times. The three positions are shown as:
cube-dice-43


AC

BD

CE

DF

ENone of these

Answer: Option C

Explanation:

From figures (ii) and (iii), we conclude that the alphabets C, D, B and F appear adjacent to the alphabet E. Therefore, the alphabet A appears opposite E. Conversely, E appears opposite A.

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A dice is numbered from 1 to 6 in different ways.

If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?.PNG" alt="cube-dice-4140" style="width:288px;height:235px;">


A2 is opposite to 6

B1 is adjacent to 3

C3 is adjacent to 5

D3 is opposite to 5

ENone of these

Answer: Option C

Explanation:

If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).

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A dice is rolled twice and the two positions are shown in the figure below. What is the number of dots at the bottom face when the dice is in position (i)?
cube-dice-87


A1

B5

C6

DCan not be determined

ENone of these

Answer: Option C

Explanation:

From figures (i) and (ii) we conclude that 3, 4, 1 and 5 dots appear adjacent to 2 dots. Therefore, 6 dots must appear opposite 2 dots. Since, there are 2 dots on the top face when the dice is in position (i), therefore, the number of dots at the bottom face must be 6.

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